Your question is a bit unclear , but I will try and see if I can understand.

- If you can answer the following question for me, then perhaps, I will have
some idea of where your question is coming from, and may be I can respond next
time.

Why are you applying double integral on a ONE-Dimensional function such as a
straight line? You only do double integral (2-dimensional space) if you have a
function in 2 variables. Straight line is a function is one-dimensional space,
and therefore use single integral rather than double. This concept can be
extended to n-dimensional space. You can have 3, 4, 5, 6, ... , nth integral.
This sort of integrals you usually find in Physics and Engineering problems,
such as "Continuum Mechanics" , that is fluid mechanics. You usually encounter
problems to solve with 4, 5 or 6 integrals. The usual method of solving is SOR
(Succesive Over Relaxation) and QUAD (Quadrature).

This material is based upon work supported by the
National Science Foundation under Grant DUE-0226284.
Any opinions, findings, and conclusions or recommendations
expressed in this material are those of the author(s)
and do not necessarily reflect the views of the
National Science Foundation.